What is distinctive about the way Novak Djokovic or Roger Federer serves? What makes serves similar and what makes them different?

These questions refer to the 'playing style' of each player. We focus on the tennis serve due to it's importance in a tennis game as the first serve alone allows top male tennis players to win more than 80% of these points in a game.

(Johnson & McHugh, 2006)

The data set contains a sample of 2000 serves from the 2015 Australian Open Tournament.

The serves are given by 2 Arc's, given by a function for the X,Y,Z position of the ball across time.

Arc 1: A Polynomial from the impact of the serve to when hits the ground.

Arc 3: A Polynomial from where it hit the ground to where the ball either meets the opponents racket, or end point if an ace.

Other data is also provided for each serve, ranging from server and receiver characterstics, speed, starting position, net clearance to the point characteristics or situation in the game when a serve is played.

The first questions we naturally asked is what are the types of serves a tennis player can do? Coaching literature defines a few types of serves:

• Flat serve

• Top spin serve

• Slice serve

• Kick serve

Serves are taught to players based on a few key variants that make a serve different. Generally the main things that a player can control to change the serve type is the ball toss and the way the racquet makes impact with the ball.

The type of serve is important to distinguish, but it doesn't help us explain the style of the server. To do this we incorporated more aspects of the serve to explain what makes players different when it comes to serving. Do they vary their serves? Or do they just do one or two types? What about first and second serves?

The following variabes were used to help us group the serves into different clusters: - Start Position - Speed - Height off the bounce - Net Clearance - Location of the bounce in the service box - Angle change

These variables were all scaled to give equal weighting.

These general plots give an indication that many of these variables play a role in how and where the player serves.

The angle change variable was used to incorporate the spin of the ball

The negative values arise for the way the angle change variable was calculated. These values represent an angle change from the trajectory from where the ball was hit and the trajectory after the bounce of the ball. From the data, only 14 serves changed direction. Murray contributed 6 of the 14 serves that changed direction. This mainly arose during his game against Raonic. As seen in the graphs the spin of the ball, its angle change, appears to be prominent where the speed of the ball is low. At high speed tends to be no angle change.

The first serve is longer and usually passes lower over the net. This makes sense as players have a tendency to hit safer serves on the second serve and take more risks on the first serve.

##    
##       1   2
##   0 122   6
##   1 643 481
##   2 255  99
##   3 357  37

The table highlights that there are 37 double faults in the data, 6 aces on the second serve and when filtering by first serve for clustering, an additional 357 serves will be lost.

Murray Vs Raonic Aces

Murray Vs Djokovic

To break down the serving styles and compare the similarity of serves, we ran Hierarchical Cluster Analysis. This was performed on first and second serves seperately. The variables were also standardise to ensure equal weighting was given to each of the variables.

Large proportion of serves in cluster 1. Later we found that this was viable as most first serves are fast and flat. This found to be the case in a previous paper published earlier this year.

The 3rd cluster is notably different, with the spin variable, angle direction, and height of the bounce having a large effect. When observing these serves they are seem to be kick serves that are to the Ad court side. Interestingly, these are all viable serves and the majority coming from Dominic Thiem (7 out of 17).

The same process was then done for second serves. Second serves tend to vary more, as some players opt to play riskier, while others adopt top spin and slice serves.

Cluster Stats

Principle Component Plot

• Confirmed that first serves are flat and fast with less spin variation compared to second serves.

• Variability: Although there are more clusters for the first serve, a greater proportion of these are fast serves. Unlike second serves, where there may be less clusters but they are split more evenly highlighting that one type isnt as dominant across all players.

• Playing styles could be identified by the proportion of different serves they do. This allowed us to demonstrate the different styles between powerful servers like Raonic, to more varied servers like Nishikori.

• Different Clustering methods i.e Functional Clustering

• Weighting variables accordingly

• Cluster validation

• Should just the arc, speed, spin and bounce be taken into consideration? Standardise all starting and landing positions.

• Accurate measure for spin.

• Compare cluster variation between different games and opponents to see if the player keeps to one style or changes their style according to opponent